Accelerated line-search and trust-region methods

P.-A. Absil (absilinma.ucl.ac.be)
K. A. Gallivan (gallivanscs.fsu.edu)

Abstract: In numerical optimization, line-search and trust-region methods are two important classes of descent schemes, with well-understood global convergence properties. Here we consider ``accelerated'' versions of these methods, where the conventional iterate is allowed to be replaced by any point that produces at least as much decrease in the cost function as a fixed fraction of the decrease produced by the conventional iterate. A detailed convergence analysis reveals that global convergence properties of line-search and trust-region methods still hold when the methods are accelerated. The analysis is performed in the general context of optimization on manifolds, of which optimization in R^n is a particular case. This general convergence analysis sheds a new light on the behavior of several existing algorithms.

Keywords: line search, trust region, subspace acceleration, sequential subspace method

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Applications -- Science and Engineering

Citation: http://dx.doi.org/10.1137/08072019X : SIAM Journal on Numerical Analysis, Vol. 47, No. 2, pp. 997-1018, 2009

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Entry Submitted: 04/03/2008
Entry Accepted: 04/03/2008
Entry Last Modified: 02/19/2010

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